DSpace Collection:

On the closure of cyclic subgroups of a free group in some profinite topologies

Wed, 01 Jan 2025 00:00:00 GMT

Title: On the closure of cyclic subgroups of a free group in some profinite topologies Abstract: We determine the closure of a cyclic subgroup H of a free group for the pro-V topology when V is an extension-closed pseudovariety of finite groups. We show that H is always closed for the pro-nilpotent topology and compute its closure for the pro-G(p) and pro- V-p topologies, where G(p) is the pseudovariety of finite p-groups and V-p superset of G(p) denote the pseudovarieties involved in the join decomposition of the pseudovariety of finite supersolvable groups. More generally, given any nonempty set P of primes, we consider the stated problem for the pseudovariety G(P) of all finite groups having order a product of primes in P.

Geodesic languages for rational subsets and conjugates in virtually free groups

Thu, 01 Jan 2026 00:00:00 GMT

Title: Geodesic languages for rational subsets and conjugates in virtually free groups Abstract: We prove that a subset of a virtually free group is rational if and only if the language of geodesic words representing its elements (in any generating set) is rational and that the language of geodesics representing conjugates of elements in a rational subset of a virtually free group is context-free. As a corollary, the doubly generalized conjugacy problem is decidable for rational subsets of finitely generated virtually free groups: there is an algorithm taking as input two rational subsets K1 and K2 of a virtually free group that decides whether there is one element of K1 conjugate to an element of K2. For free groups, we prove that the same problem is decidable with rational constraints on the set of conjugators. (c) 2026 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons.org/licenses/by/4.0/).

On a pseudovariety of finite supersolvable groups

Thu, 01 Jan 2026 00:00:00 GMT

Title: On a pseudovariety of finite supersolvable groups Abstract: We introduce the pseudovariety of finite groups U =boolean OR(p is an element of & Popf;)Ab(p) & lowast;Ab(p - 1), where & Popf; is the set of all primes. We show that U consists of all finite supersolvable groups with elementary abelian derived subgroup and abelian Sylow subgroups, and so U has decidable membership problem. We prove that it is decidable whether or not a finitely generated subgroup of a free group is closed or dense for the pro-U topology. We consider also the pseudovariety of finite groups Ab(p) & lowast;Ab(d) (where p is a prime and d divides p - 1). We study the pro-(Ab(p) & lowast;Ab(d)) topology on a free group and construct the unique generator of minimum size of the pseudovariety Ab(p) & lowast;Ab(d). Finally, we prove that the variety of groups generated by U is the variety of all metabelian groups, obtaining also results on the varieties generated by a Baumslag-Solitar group of the form BS(1,q) for q prime.

Maximum-expectation matching under recourse

Wed, 01 Jan 2025 00:00:00 GMT

Title: Maximum-expectation matching under recourse Abstract: This paper addresses the problem of maximizing the expected size of a matching in the case of unreliable vertices and/or edges. The assumption is that the solution is built in several steps. Ina given step, edges with successfully matched vertices are made permanent; but upon edge or vertex failures, the remaining vertices become eligible for reassignment. This process maybe repeated a given number of times, and the objective is to end with the overall maximum number of matched vertices. An application of this problem is found in kidney exchange programs, going on in several countries, where a vertex is an incompatible patient-donor pair and an edge indicates cross-compatibility between two pairs; the objective is to match these pairs so as to maximize the number of served patients. A new scheme is proposed for matching rearrangement in case of failure, along with a prototype algorithm for computing the optimal expectation for the number of matched edges (or vertices), considering a possibly limited number of rearrangements. Computational experiments reveal the relevance and limitations of the algorithm, in general terms and for the kidney exchange application.

Modeling the Effect of Intravenous Anesthetics: A Path Toward Individualization

Thu, 01 Jan 2015 00:00:00 GMT

Title: Modeling the Effect of Intravenous Anesthetics: A Path Toward Individualization Abstract: The path from complex pharmacokinetic/pharmacodynamic (PK/PD) models to reduced models that allow for runtime parameter estimation and provide good runtime prediction capabilities in the closed-loop cyber-physical system (CPSs) delivering the anesthesia is reported. The path from the administered amount of drug to the measured effect is hence divided into two parts, the pharmacokinetics (PK) and the pharmacodynamics (PD). Due to the fact that the majority of the PK of the drugs can be captured by linear time-invariant (LTI) dynamics, and the PD includes a static nonlinearity, a Wiener model has become a popular choice. The method to obtain population models relies on regressions made on collected blood samples from patients at different instants after administration of anesthetics. In the first step, individual estimates of the PK/PD parameters are obtained as empirical Bayesian estimates, based on a prior using no covariates. In the second step, the individual PK/PD parameter estimates are regressed on the covariates using a generalized additive model. In the third and final step, the software NONMEM is used to optimize the population model. More recently, a reduced model for the hypnosis-remifentanil-induced DoA with only four parameters was proposed in and its performance compared with other complex model structures.

Heuristics and exact methods for number partitioning

Fri, 01 Jan 2010 00:00:00 GMT

Title: Heuristics and exact methods for number partitioning Abstract: Number partitioning is a classical NP-hard combinatorial optimization problem, whose solution is challenging for both exact and approximative methods. This work presents a new algorithm for number partitioning, based on ideas drawn from tree search, breadth first search, and beam search. A new set of benchmark instances for this problem is also proposed. The behavior of the new method on this and other testbeds is analyzed and compared to other well known heuristics and exact algorithms.

A Deleting Derivations Algorithm for Quantum Nilpotent Algebras at Roots of Unity

Mon, 01 Jan 2024 00:00:00 GMT

Title: A Deleting Derivations Algorithm for Quantum Nilpotent Algebras at Roots of Unity Abstract: This paper extends an algorithm and canonical embedding in [6] to a large class of quantum algebras. It applies to iterated Ore extensions over a field satisfying some suitable assumptions which cover those of Cauchons original setting but also allows for roots of unity. The extended algorithm constructs a quantum affine space A from the original quantum algebra A via a series of change of variables within the division ring of fractions Frac(A). The canonical embedding takes a completely prime ideal P A to a completely prime ideal Q A such that when A is a PI algebra, PI-deg(A/P) = PI-deg(A/Q). When the quantum parameter is a root of unity, combining our construction with results from [2] allows us to state an explicit formula for the PI degree of completely prime quotient algebras. This paper ends with a method to construct a maximum dimensional irreducible representation of A/P given a suitable irreducible representation of A/Q when A is PI. (c) The authors, 2024.

The geometric classification of nilpotent algebras

Sun, 01 Jan 2023 00:00:00 GMT

Title: The geometric classification of nilpotent algebras Abstract: We give a geometric classification of n-dimensional nilpotent, commutative nilpotent and anticommutative nilpotent al-gebras. We prove that the corresponding geometric varieties are irreducible, find their dimensions and describe explicit generic families of algebras which define each of these varieties. We show some applications of these results in the study of the length of anticommutative algebras. & COPY; 2023 The Author(s). Published by Elsevier Inc. This is an open access article under the CC BY license (http:// creativecommons .org /licenses /by /4 .0/).

A classification of nilpotent compatible Lie algebras

Wed, 01 Jan 2025 00:00:00 GMT

Title: A classification of nilpotent compatible Lie algebras Abstract: Working over an arbitrary field of characteristic different from 2, we extend the Skjelbred-Sund method to compatible Lie algebras and give a full classification of nilpotent compatible Lie algebras up to dimension 4. In case the base field is cubically closed, we find that there are three isomorphism classes and a one-parameter family in dimension 3, and 12 isomorphism classes, 6 one-parameter families and one 2-parameter family in dimension 4.

Representations of Smith algebras which are free over the Cartan subalgebra

Mon, 01 Jan 2024 00:00:00 GMT

Title: Representations of Smith algebras which are free over the Cartan subalgebra Abstract: In this paper, we study the category of modules over the Smith algebra which are free of finite rank over the unital polynomial subalgebra generated by the Cartan element h and obtain families of such simple modules of arbitrary rank. In the case of rank one we obtain a full description of the isomorphism classes, a simplicity criterion, and an algorithm to produce all composition series. We show that all such modules have finite length and describe the composition factors and their multiplicity.

Leibniz algebras and graphs

Sun, 01 Jan 2023 00:00:00 GMT

Title: Leibniz algebras and graphs Abstract: We consider a Leibniz algebra L = J circle plus D over an arbitrary base field F, being J the ideal generated by the products [x,x],x is an element of L. This ideal has a fundamental role in the study presented in our paper. A basis B = {v(i)}(i is an element of I) of L is called multiplicative if for any i,j is an element of I we have that [v(i), v(j)] is an element of Fv(k) for some k is an element of I. We associate an adequate graph Gamma (L, B) to L relative to B. By arguing on this graph we show that L decomposes as a direct sum of ideals, each one being associated to one connected component of Gamma(L, B). Also the minimality of L and the division property of L are characterized in terms of the weak symmetry of the defined subgraphs Gamma(L, B-J) and Gamma (L, B-D).

Noncommutative algebra and representation theory: symmetry, structure invariants

Mon, 01 Jan 2024 00:00:00 GMT

Title: Noncommutative algebra and representation theory: symmetry, structure invariants Abstract: This is an abridged version of our Habilitation thesis. In these notes, we aim to summarize our research interests and achievements as well as motivate what drives our work: symmetry, structure and invariants. The paradigmatic example which permeates and often inspires our research is the Weyl algebra A1 .

The algebraic classification of nilpotent algebras

Sat, 01 Jan 2022 00:00:00 GMT

Title: The algebraic classification of nilpotent algebras Abstract: We give the complete algebraic classification of all complex 4-dimensional nilpotent algebras. The final list has 234 (parametric families of) isomorphism classes of algebras, 66 of which are new in the literature.

Kunz languages for numerical semigroups are context sensitive

Thu, 01 Jan 2026 00:00:00 GMT

Title: Kunz languages for numerical semigroups are context sensitive Abstract: There is a one-to-one and onto correspondence between the class of numerical semigroups of depth n, where n is an integer, and a certain language over the alphabet {1, , n}, which we call a Kunz language of depth n. The Kunz language associated with the numerical semigroups of depth 2 is the regular language {1, 2}2{1, 2}. We prove that Kunz languages associated with numerical semigroups of larger depth are context-sensitive but not regular. (c) 2026 MSP (Mathematical Sciences Publishers).

A verification of Wilf's conjecture up to genus 100

Wed, 01 Jan 2025 00:00:00 GMT

Title: A verification of Wilf's conjecture up to genus 100 Abstract: For a numerical semigroup S subset of N, let m,e,c,g denote its multiplicity, embedding dimension, conductor and genus, respectively. Wilf's conjecture (1978) states that e(c-g)>= c. As of 2023, Wilf's conjecture has been verified by computer up to genus g <= 66. In this paper, we extend the verification of Wilf's conjecture up to genus g <= 100. This is achieved by combining three main ingredients: (1) a theorem in 2020 settling Wilf's conjecture in the case e >= m/3, (2) an efficient trimming of the tree T of numerical groups identifying and cutting out irrelevant subtrees, and (3) the implementation of a fast parallelized algorithm to construct the tree T up to a given genus. We further push the verification of Wilf's conjecture up to genus 120 in the particular case where m divides c. Finally, we unlock three previously unknown values of the number ng of numerical semigroups of genus g, namely for g=73,74,75. (c) 2024 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

Epidemiology and the Bologna saga

Thu, 01 Jan 2004 00:00:00 GMT

Title: Epidemiology and the Bologna saga

On sufficient conditions for the transitivity of homeomorphisms

Thu, 01 Jan 2026 00:00:00 GMT

Title: On sufficient conditions for the transitivity of homeomorphisms

Dual action of benzaldehydes: Inhibiting quorum sensing and enhancing antibiotic efficacy for controlling Pseudomonas aeruginosa biofilms

Mon, 01 Jan 2024 00:00:00 GMT

Title: Dual action of benzaldehydes: Inhibiting quorum sensing and enhancing antibiotic efficacy for controlling Pseudomonas aeruginosa biofilms Abstract: Quorum sensing (QS) has a central role in biofilm lifestyle and antimicrobial resistance, and disrupting these signaling pathways is a promising strategy to control bacterial pathogenicity and virulence. In this study, the efficacy of three structurally related benzaldehydes (4-hydroxybenzaldehyde, 4-hydroxy-3-methoxybenzaldehyde (vanillin) and 4-hydroxy-3,5-dimethoxybenzaldehyde (syringaldehyde)) in disrupting the las and pqs systems of Pseudomonas aeruginosa was investigated using bioreporter strains and computational simulations. Additionally, these benzaldehydes were combined with tobramycin and ciprofloxacin antibiotics to evaluate their ability to increase antibiotic efficacy in preventing and eradicating P. aeruginosa biofilms. To this end, the total biomass, metabolic activity and culturability of the biofilm cells were determined. In vitro assays results indicated that the aromatic aldehydes have potential to inhibit the las and pqs systems by > 80 %. Molecular docking studies supported these findings, revealing the aldehydes binding in the same pocket as the natural ligands or receptor proteins (LasR, PQSA, PQSE, PQSR). Benzaldehydes were shown to act as virulence factor attenuators, with vanillin achieving a 48 % reduction in pyocyanin production. The benzaldehyde-tobramycin combination led not only to a 60 % reduction in biomass production but also to a 90 % reduction in the metabolic activity of established biofilms. A similar result was observed when benzaldehydes were combined with ciprofloxacin. 4-Hydroxybenzaldehyde demonstrated relevant action in increasing biofilm susceptibility to ciprofloxacin, resulting in a 65 % reduction in biomass. This study discloses, for the first time, that the benzaldehydes studied are potent QS inhibitors and also enhancers of antibiotics antibiofilm activity against P. aeruginosa.

Efficacy of Novel Quaternary Ammonium and Phosphonium Salts Differing in Cation Type and Alkyl Chain Length against Antibiotic-Resistant Staphylococcus aureus

Mon, 01 Jan 2024 00:00:00 GMT

Title: Efficacy of Novel Quaternary Ammonium and Phosphonium Salts Differing in Cation Type and Alkyl Chain Length against Antibiotic-Resistant Staphylococcus aureus Abstract: Antibacterial resistance poses a critical public health threat, challenging the prevention and treatment of bacterial infections. The search for innovative antibacterial agents has spurred significant interest in quaternary heteronium salts (QHSs), such as quaternary ammonium and phosphonium compounds as potential candidates. In this study, a library of 49 structurally related QHSs was synthesized, varying the cation type and alkyl chain length. Their antibacterial activities against Staphylococcus aureus, including antibiotic-resistant strains, were evaluated by determining minimum inhibitory/bactericidal concentrations (MIC/MBC) <= 64 mu g/mL. Structure-activity relationship analyses highlighted alkyl-triphenylphosphonium and alkyl-methylimidazolium salts as the most effective against S. aureus CECT 976. The length of the alkyl side chain significantly influenced the antibacterial activity, with optimal chain lengths observed between C-10 and C-14. Dose-response relationships were assessed for selected QHSs, showing dose-dependent antibacterial activity following a non-linear pattern. Survival curves indicated effective eradication of S. aureus CECT 976 by QHSs at low concentrations, particularly compounds 1e, 3e, and 5e. Moreover, in vitro human cellular data indicated that compounds 2e, 4e, and 5e showed favourable safety profiles at concentrations <= 2 mu g/mL. These findings highlight the potential of these QHSs as effective agents against susceptible and resistant bacterial strains, providing valuable insights for the rational design of bioactive QHSs.

First Insight into Lignin Valorization as a Promising Biopolymer for the Modulation of the Physicochemical Properties of Port Wine

Mon, 01 Jan 2024 00:00:00 GMT

Title: First Insight into Lignin Valorization as a Promising Biopolymer for the Modulation of the Physicochemical Properties of Port Wine Abstract: Lignosulfonate (LS), kraft lignin (KL), and organosolv lignin (OL) were evaluated as potential modulating agents of the physicochemical properties of Port wine at two different concentrations for 7 and 30 days. KL and LS demonstrated the ability to remove proteins and potentiate the anthocyanin concentration. LS reduced the tannin content and the interaction of salivary acidic proline-rich proteins with wine phenolic compounds. None of the lignin promoted a perceptible color change; however, the yellowish color of KL and OL at 100 g/hL contributed to an increase in the yellow tones of wines. Lignin improved wine aroma by reducing the amount of unwanted volatiles by 30% and increasing the content of ethyl esters associated with fruity aromas by up to 60%. The results suggest that lignin, especially LS, can be employed as a modulating agent, positively impacting wine's physicochemical properties. This valorization of a byproduct opens up new opportunities for the wine industry.